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After a brief comparison of Aliseda’s account with different approaches to abductive reasoning, I relate abduction, as studied by Aliseda, to idealization, a notion which also occupies a very important role in scientific change, as well as to different ways of dealing with the growth of scientific knowledge understood as a particular kind of non-monotonic process. A particularly interesting kind of abductive reasoning could be that of finding an appropriate concretization case for a theory, originally revealed as extraordinarily successful but later discovered to be strictly false or only approximately or ideally true. I try to show this with the example of the Kepler-Newton relation. At the end of the paper, I give criteria in order to construe abductive explanations in correspondence with a reasonable account of empirical progress.